NCAP-10: A Unified, Invariant, Geometry-Based Measurement Theory for Machine Cognition

NCAP-10 is a closed-form, architecture-invariant measurement theory for machine cognition. It defines a single manifold-valued object N = (X,p(m | d),gI,T ) from which all cognitive scores, difficulty coordinates, and invariants are derived. The framework draws on modern information geometry, scaling-law research, alignment and safety literature, and neuromorphic computation. This paper presents the final closed mathematical form of NCAP-10, its invariance axioms, and its commercial utility for evaluating heterogeneous AI systems.